How do I batch-rename objects/paths (not just layers)?

Question

Question from a complete n00b:
I need to rename a large number of selected objects/paths. This is because I want to use another script that only works when my objects have the default name, "<Path>". So really, I just need to remove existing names of objects.
This other script is here:
http://kelsocartography.com/blog/?p=325
Of course, I could manually remove names by double-clicking on objects in the layers palette and deleting the name, but that's no fun.
I've found some great scripts for renaming layers, but nothing for non-layer objects.
First, I'm trying to remove names from ALL objects in the document.  once that's working, I want to only remove names of selected objects.
Here's my very simple non-working javascript - (the whole thing):
app.activeDocument.pageItem.name = "";
my test Ai file is also really basic: a few rectangles, some of which have been named in the layers palette.
When I run this, I get:
Error 21: undefined is not and object.
Line: 1
->     app.activeDocument.pageItem.name = "";
I've tried a number of other approaches, and either get "undefined is not an object" or nothing happens. 
pageItem has "name" as a writable property, so I think it's what to use, but I really don't know what I'm doing - help!
I'd also happy to use actions, but I'm stuck on that too.

Answer 1

Thanks!!
Here's my final script:
////START SCRIPT////
//how to use: select objects that you want to rename, then run script
//note - new name may not display until you unselect objects
var docRef = activeDocument;
for (var i=0; i < docRef.pageItems.length; i++)
       if (docRef.pageItems[i].selected == true)
               docRef.pageItems[i].name = "";
////END SCRIPT////
currently, it renames with no text.  In other words, it removes existing names.
One thing that was messing me up was that new names are not immediately displayed - you have to unselect your selected objects before names in the layers palette refresh.